Hurst exponent estimation of locally self-similar Gaussian processes using sample quantiles

Details Hurst exponent estimation of locally self-similar Gaussian processes using sample quantiles Hurst exponent estimation of locally self-similar Gaussian processes using sample quantiles

2005-06-15

arxiv.org/abs/math/0506290v2

Mathematics

Statistics Theory

44 pages, f\'{e}vrier 2007

Scientific paper

This paper is devoted to the introduction of a new class of consistent estimators of the fractal dimension of locally self-similar Gaussian processes. These estimators are based on convex combinations of sample quantiles of discrete variations of a sample path over a discrete grid of the interval $[0,1]$. We derive the almost sure convergence and the asymptotic normality for these estimators. The key-ingredient is a Bahadur representation for sample quantiles of non-linear functions of Gaussians sequences with correlation function decreasing as $k^{-\alpha}L(k)$ for some $\alpha>0$ and some slowly varying function $L(\cdot)$.

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